Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int32_t main() {
  long long n;
  cin >> n;
  vector<long long> a;
  long long num = 1, diff = 2;
  while (num <= n) {
    a.push_back(num);
    num = num + diff;
    diff++;
  }
  long long s = a.size();
  for (long long i = 0; i < s; i++) {
    if (binary_search(a.begin() + i, a.end(), n - a[i])) {
      cout << "YES\n";
      return 0;
    }
  }
  cout << "NO\n";
  return 0;
}